List of top Mathematics Questions asked in JEE Main

If \(\alpha\) and \(\beta\) are the roots of the equation \(375x^2 - 25x - 2 = 0\), then \(\lim_{n\to\infty}\sum_{r=1}^{n}\alpha^r + \lim_{n\to\infty}\sum_{r=1}^{n}\beta^r\) is equal to :

The equation \(|z - i| = |z - 1|\), \(i = \sqrt{-1}\), represents :

If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = \(\begin{bmatrix} 2 & 3 \\ 5 & -1 \end{bmatrix}\), then AB is equal to :

The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is :

If \(B = \begin{bmatrix} 5 & 2\alpha & 1 \\ 0 & 2 & 1 \\ \alpha & 3 & -1 \end{bmatrix}\) is the inverse of a \(3 \times 3\) matrix A, then the sum of all values of \(\alpha\) for which det(A) + 1 = 0, is :

If the data \(x_1, x_2, \ldots\ldots, x_{10}\) is such that the mean of first four of these is 11, the mean of the remaining six is 16 and the sum of squares of all of these is 2,000 ; then the standard deviation of this data is :

If m is the minimum value of k for which the function \(f(x) = x\sqrt{kx - x^2}\) is increasing in the interval [0,3] and M is the maximum value of f in [0, 3] when k = m, then the ordered pair (m, M) is equal to :

If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is :

Consider the differential equation, \(y^2\,dx + \left(x - \frac{1}{y}\right)dy = 0\), If value of y is 1 when x = 1, then the value of x for which y = 2, is :

The value of \(\sin^{-1}\left(\frac{12}{13}\right) - \sin^{-1}\left(\frac{3}{5}\right)\) is equal to :

If \(\int_0^{\pi/2} \frac{\cot x}{\cot x + \operatorname{cosec} x}\,dx = m(\pi + n)\), then \(m \cdot n\) is equal to

If the plane \(2x-y+2z+3=0\) has the distances \(\frac13\) and \(\frac23\) units from the planes \(4x-2y+4z+\lambda=0\) and \(2x-y+2z+\mu=0\), respectively, then the maximum value of \(\lambda+\mu\) is equal to :

If the tangent to the curve \(y=\frac{x}{x^2-3}\), \(x\in\mathbb{R},\ (x\ne\pm\sqrt3)\), at a point \((\alpha,\beta)\ne(0,0)\) on it is parallel to the line \(2x+6y-11=0\), then :

If the line \(ax+y=c\), touches both the curves \(x^2+y^2=1\) and \(y^2=4\sqrt{2}\,x\), then \(|c|\) is equal to :

The negation of the Boolean expression \(\sim s \vee (\sim r \wedge s)\) is equivalent to :

If \(5x+9=0\) is the directrix of the hyperbola \(16x^2-9y^2=144\), then its corresponding focus is :

The smallest natural number n, such that the coefficient of x in the expansion of \(\left(x^2+\frac{1}{x^3}\right)^n\) is \(^{n}\mathrm{C}_{23}\), is :

The locus of the centres of the circles, which touch the circle, \(x^2+y^2=1\) externally, also touch the y-axis and lie in the first quadrant, is :

The angles A, B and C of a triangle ABC are in A.P. and \(a:b=1:\sqrt{3}\). If \(c=4\) cm, then the area (in sq. cm) of this triangle is :

A perpendicular is drawn from a point on the line \(\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z}{1}\) to the plane \(x+y+z=3\) such that the foot of the perpendicular Q also lies on the plane \(x-y+z=3\). Then the co-ordinates of Q are :

Lines are drawn parallel to the line \(4x-3y+2=0\), at a distance \(\dfrac35\) from the origin. Then which one of the following points lies on any of these lines ?

If both the mean and the standard deviation of 50 observations \(x_1,x_2,\ldots,x_{50}\) are equal to 16, then the mean of \((x_1-4)^2,(x_2-4)^2,\ldots,(x_{50}-4)^2\) is :

Let \(y=y(x)\) be the solution of the differential equation \(\dfrac{dy}{dx}+y\tan x=2x+x^2\tan x\), \(x\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)\), such that \(y(0)=1\). Then :

The area (in sq. units) of the region bounded by the curves \(y=2^x\) and \(y=|x+1|\), in the first quadrant is :

If \(\cos^{-1}x-\cos^{-1}\dfrac{y}{2}=\alpha\), where \(-1\le x\le1\), \(-2\le y\le2\), \(x\le\dfrac{y}{2}\), then for all \(x,y\), \(4x^2-4xy\cos\alpha+y^2\) is equal to :